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  • If the digits 1, 2, 3, 4, 5, 6, and 7 are used to form a seven-digit number, how many different numbers can be created by swapping the positions of any two digits?

If the digits 1, 2, 3, 4, 5, 6, and 7 are used to form a seven-digit number, how many different numbers can be created by swapping the positions of any two digits?

 

Option: 1

2512

 


Option: 2

8965

 


Option: 3

3250

 


Option: 4

5040


Answers (1)

best_answer

To find the number of different seven-digit numbers that can be created by swapping the positions of any two digits from the digits 1,2,3,4,5,6, and 7 , we need to consider the different arrangements that result from swapping the positions of any two digits.

Since there are seven digits, there are a total of 7 choices for the first digit. After choosing the first digit, there are 6 remaining digits to choose from for the second digit. Similarly, there are 5 choices for the third digit, 4 choices for the fourth digit, 3 choices for the fifth digit, 2 choices for the sixth digit, and 1 choice for the seventh digit.

Therefore, the total number of different seven-digit numbers that can be formed is

7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1=5040.

It is important to note that swapping the positions of two digits does not affect the number of different numbers that can be formed in this case, as all seven digits are distinct.

Posted by

Kuldeep Maurya

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